Cumulative distribution

A cumulative distribution answers "at most" questions by stacking probabilities from the bottom up, so it climbs from 0 to 1 and never falls. If $X$ is the number of heads in two fair coin flips, with $P(0) = 0.25$, $P(1) = 0.50$, and $P(2) = 0.25$, the cumulative values are $0.25$, $0.75$, and $1$. In symbols, $F(x) = P(X \le x) = \sum_{x_i \le x} P(x_i)$ (the probability X is less than or equal to x). The cdf commands on a graphing calculator compute exactly this, which is why they answer "at most" questions but not "exactly" questions.